The present invention relates to the measurement of birefringence, particularly the optical characterization of retardation and eigenpolarization of an unknown retarding device.
The optical characterization of retarding devices, sometimes referred to as birefringent devices, is a well-known problem in crystal optics. An important area where such characterization is needed is in the field of liquid crystals. A retarding device is fully characterized when the state of polarization of light passing through the device can be predicted as a function of the state of polarization incident onto the device and as a function of the eigenpolarization and retardation of the retarding device itself. The main task is to determine the eigenpolarization and the retardation of the retarding device experimentally.
There are numerous solutions for this problem with different problems and restrictions. They can be split into three families: the family of conoscopic methods; the family of Stokes parameter methods; and the family of liquid crystal waveguide methods.
In one family of conoscopic methods of characterization, light of a known polarization is sent through the retarding device sample and the changes of polarization as a function of the direction of the light beam are analyzed by a fixed analyzer. Such methods include the classical conoscopic method (see R. E. Stoiber, Crystal Identification with the polarizing microscope, Chapman and Hall, New York, 1994), the scanning conoscopic method (see Warenghem, M. and Grover, C. P., Scanning conoscopy: a novel method for birefringent samples, Molecular Crystal and Liquid Crystal, 1988, vol. 159, pp. 15-25), and the crystal rotation method (see E. E. Wahlstrom, Optical crystallography, Wiley, 1979). In another family of conoscopic methods, light of known polarization is sent through the retarding device and the changes of polarization as a function of the wavelength are analyzed by a fixed analyzer. Changes in polarization result in an intensity signal which is then quantified or recorded by some means, for example by naked eye, photographic camera, or with a photodetector. These methods do not work for all kinds of retarding device. If the retarding device is below a certain thickness, the intensity signal shows too little variation and the results for the eigenpolarization and the retardation will be associated with huge error bars. For example, in the case of a liquid crystal, the sample thickness must be thicker than 10 xcexcm. In general, conoscopic methods are not applied to retarding devices with complicated internal structures, for example twisted nematic liquid crystals.
With Stokes parameter methods of characterization, light of a known polarization is sent through the retarding device and the change of polarization is analyzed by a set of measurements with different polarizers. The classic method (see D. S. Kliger et al., Polarized light in optics and spectroscopy, Academic Press, Boston, 1990) requires six measurements with a linear analyzer at 0xc2x0 (horizontal), 90xc2x0 (vertical), 45xc2x0, 135xc2x0, and also with a right-handed circular polarizer and a left-handed circular polarizer. Almost all realizations of Stokes parameter measurements are relatively slow and cannot be adapted for real-time measurements. The newest implementation of a Stokes parameter measurement (see Liu, J., Azzam, R. M. A., Corner-cube four-detector photopolarimeter, Optics and Laser Technology, 1997, vol. 29, pp. 233-238) exploits the Brewster angle and does allow, for the first time, real-time measurements. But all such methods suffer from the limitation of being are very sensitive to misalignments. Therefore, the accuracy of the results is either not very high or the data collection time is long.
The liquid crystal waveguide methods (see the article by Fuzi Yang et al, Guided modes and related optical techniques in liquid crystal alignment studies, in the publication edited by S. Elston and R. Sambles, The optics of thermotropic liquid crystals, Taylor and Francis, London, 1998) are the most elaborate and also produce the most exact results. However, these methods are also difficult to implement and time consuming to perform. Sometimes, these require a specially modified sample, but always involve a complicated and time-consuming calculations for fitting data to equations describing the method.
It is an object of the present invention to provide a more convenient device and method for optically characterizing the retardation and eigenpolarization of an unknown birefringent sample.
According to the invention, there is provided a method of optically characterizing the retardation and eigenpolarization of an unknown retarding device, comprising the steps of:
a) generating an optical probe beam with a pre-determined polarization;
b) splitting the probe beam into two components, with constant dynamic phase difference;
c) passing each of the two probe beam components through the retarding device in opposite directions so that the polarization of each probe beam component is retarded by an equal degree, but the directions of the optic axis have opposite signs for the two probe beams.
d) passing the retarded probe beam components together through a polarizing analyzer with a pre-determined polarization axis to resolve the polarization of each retarded probe beam component along said axis;
e) receiving the polarization resolved beams on an optical detector so that said beams maintain the same dynamic phase and interfere coherently depending on the geometric phase between the two interfering polarization resolved beams; and
f) using the detector to measure the interference between the two interfering polarization resolved beams;
wherein the angle of the polarization axis of the analyzer is rotated to resolve the polarization of each of the polarization resolved beams along said rotating axis, in order to vary the geometric phase and hence the measured interference from the detector, the measured varying interference being used to calculate the retardation and eigenpolarisation of the unknown retarding device.
Also according to the invention, there is provided an apparatus for optically characterizing the retardation and eigenpolarization of an unknown retarding device, comprising:
a) an optical source for generating an optical probe beam with a pre-determined polarization;
b) a beam splitter for splitting the probe beam into two components, with constant dynamic phase difference between the components, the retarding device being arranged to receive from opposite directions each of the two probe beam components so that the polarization of each probe beam component is retarded by an equal degree;
d) a polarizing analyzer arranged to receive both the retarded probe beam components, the analyzer having a pre-determined polarization axis to resolve the polarization of each of the retarded probe beam components along said axis;
e) an optical detector arranged to receive the polarisation resolved beams so that said beams maintain the same dynamic phase and interfere coherently depending on a different geometric phase between the two polarization resolved beams, and to measure therefrom said interference;
f) means for rotating the angle of the polarization axis of the analyzer to resolve the polarization of each beam along said rotating axis and to vary the geometric phase between the two polarization resolved beams;
wherein the apparatus includes means for rotating the angle of the polarization axis of the analyzer to resolve the polarization of each of the polarization resolved beams along said rotating axis, in order to vary the geometric phase and hence the measured interference from the detector, the measured varying interference being used by a processor to calculate the retardation and eigenpolarisation of the unknown retarding device.
The concept of the xe2x80x9cgeometric phasexe2x80x9d is best understood with reference to the Poincarxc3xa9 sphere, and will be further described in the description relating to the drawings.
Although the two probe beam components pass through the retarding device in opposite directions so that the polarization of each probe beam component is retarded by an equal degree, the directions of the optic axis for the two beams have opposite signs.
In a preferred embodiment of the invention, the measured varying interference is fit to a mathematical model of the interference between the polarization resolved beams resulting from the varying geometric phase in order to deduce the retardation and eigenpolarisation of the unknown retarding device.
It is advantageous if the method is performed using a ring interferometer. The retarding device can then be positioned in the ring, with the two probe beam components circulating around the ring and through the retarding device in opposite directions. This arrangement helps to ensure that the dynamic phase for each of the components is the same, so that essentially only the geometric phase contributes to the interference measured on the detector.
Preferably, the optical probe beam enters the interferometer through an entrance polarizer with a predetermined optical axis. The probe beam is then split by a beam splitter into said two components. The beam splitter can also be arranged to direct each component around the ring in opposite directions. After passing through and being retarded by the unknown retarding device, the two retarded probe beam components are then recombined and directed out of the ring towards the polarizing analyzer. Such an arrangement uses a small number of optical components, and is relatively inexpensive to construct and operate.
One way to form a ring interferometer is with a plurality of plane mirrors. In order to minimize polarization shifts polarization-preserving components are used and the pre-determined polarisation in the entrance of the interferometer is either horizontal or vertical.